So, I the question of what if a black hole hits the earth has been asked to death by various people, but what if the somewhat tamer wormhole hits the Earth?

In particular, we'll say that one mouth is floating somewhere in free space, and the other falls into Earth's gravity well. The radius of the mouths is 1 meter.

Note, that I am talking about a traversable wormholes, as described by general relativity (note that they are predicted to not exist in our universe (hence the alien-geometry tag), but are very well understood in the framework of general relativity). In particular, we are talking about an Ellis wormhole. Here's a video in which physicists simulate one. Note in particular that "real" wormholes are very different from the wormholes usually presented in fiction. For example, they have spherical ends instead of circular ones.

$\begingroup$The wormholes described are just black holes and will look exactly like black holes from Earth's point of view until you fall through them.$\endgroup$
– A. C. A. C.Jan 23 '18 at 19:31

3

$\begingroup$@A.C.A.C. An Ellis or Morris-Thorne wormhole is horizonless and singularity free. Schwarzschild wormholes (Eistein-Rosen Bridge) are the ones that look like black holes. Such a horizonless/singularity-free wormhole is the model used for the movie Interstellar.$\endgroup$
– guildsbountyJan 23 '18 at 19:44

1

$\begingroup$It should be noted that most people agree that Schwarzschild wormholes are non-traversable, because they immediately collapse and all objects nearby are obliterated. The only way to keep a Schwarzschild wormhole open is to stabilize it with objects of negative energy density (I'm not sure if that's a thing that exists scientifically yet).$\endgroup$
– Ben SchwabeJan 23 '18 at 20:52

2

$\begingroup$@guildsbounty Nice to see someone talking sense about wormholes for a change. Ellis wormholes deserve more love, while Morris-Thorne ones hog the limelight. Well done.$\endgroup$
– a4androidJan 24 '18 at 6:01

3

$\begingroup$And not just negative energy, @BenSchwabe but LOTS of it. Last I recall, using some for a Warp Drive to transport "a handful of atoms" would require an amount of negative energy equivalent to the mass-energy of the moon. (Also, negative energy density, aka the Casimir effect, has been proven. It was first experimentally shown in 1997 by Steve Lamoreaux).$\endgroup$
– Draco18sJan 24 '18 at 7:47

Now let me tell you something about Jupiter. From the second link in the paragraph above:

Jupiter is by far the most massive planet in the solar system. It is approximately 2.5 times more massive than all of the other planets in the Solar System combined.

What this means is that if you threw Mercury, Venus, Mars, Saturn, Uranus and Neptune against the Earth, with all of them colliding at the same time... It would still deal a few orders of magnitude less damage than that wormhole.

Suppose it does not impact on Earth. The very passage of that wormhole through our solar system in a flyby trajectory with a perihelion low enough to intersect Earth's orbit would be enough to end all life here. It would destabilize all planets' orbits. The pull on Earth would break the tectonic plates. We would see hitherto unseen extreme earthquakes and volcanic eruptions all around the globe, with the latter covering the skies with ash and toxic smoke. And in the very least Earth's orbit would become much more excentric in the aftermath, so any survivors either calcinate in a super summer or freeze in a super winter. In both scenarios, only microbes would have a chance of survival, and it might not be a good chance.

You probably wanted this question answered with a focus on the traversability of the wormhole, should it touchdown on Earth.

Well... An impactor with the mass of the Moon could probably make its way through more than half of the way to the planet core. An impactor with the mass of Jupiter might just go through the Earth from one side to the other like a rifle bullet going through a person.

Unlike a bullet though, the wormhole will drag Earth along its path due to its massive gravity. Remember, that beast has almost 318 Earth masses.

The distant mouth - the one that did not impact Earth - will spill a lot of planetary mantle, along with some planetary core and crust (and impurities such as gases, maybe a small part of the oceans, and a lot of organic material) at speeds measured in kilometers per second. Some bits have enough speed to escape the gravity of the wormhole.

On the side that did impact Earth... Well, the impact burst Earth to pieces like an egg that fell from an airplane. Most pieces will trail behind the wormhole, and given some millions or billions of years they may settle as a ring system around it. Some pieces are lost and will either orbit the Sun as comets or escape the solar system altogether.

$\begingroup$This would suggest that if you formed a wormhole in space, it would start to accumulate matter, and in very short times become "clogged" with matter that can't escape its gravity and piled around the mouths of the wormhole. Then you are basically just dealing with a miniature black hole.$\endgroup$
– ArtisticPhoenixFeb 4 '18 at 6:01

$\begingroup$The whole point of "negative energy" that it generates negative gravity, which repels objects gravitationally. So a negative energy bullet with a mass equivalent of Jupiter wouldn't drag Earth along, it would push it away with the force of Jupiter's gravity. That is, if the negative energy affects things outside the wormhole, which I'm not quite sure about.$\endgroup$
– IndigoFenixFeb 4 '18 at 8:22

1

$\begingroup$@indogofenix it is more complex than that. A positive mass and a negative mass acting on each other gravitationally would experiment a phenomenon called "the runaway effect", and could potentially accelerate towards each other up to relativistic speeds. The "negative gravity" effect of negative mass would only ever happen on two different bodies if both have negative mass. Even this is not consensus among scientists... Most likely a body imbued with negative energy such as a wormhole would have regular ADM mass, which would be positive.$\endgroup$
– RenanFeb 4 '18 at 12:52

$\begingroup$@artisticphoenix we would have to calculate its event horizon radius to see... If it is smaller than the wormhole then it is not a proper black hole.$\endgroup$
– RenanFeb 4 '18 at 13:06

$\begingroup$@Renan - I can do that I just need the mass and radius. Schwarzschild radius isn't terribly difficult.$\endgroup$
– ArtisticPhoenixFeb 4 '18 at 21:39

Disregarding the mass/energy issue (where a wormhole weighs an insane amount). We'll just assume that the physical essence (the wormhole itself) of the wormhole has no effect on the universe other then allowing 2 distant places to be linked together.

My first thought was something like a giant vacuum cleaner.

In particular, we'll say that one mouth is floating somewhere in free space, and the other falls into Earth's gravity well. The radius of the mouths is 1 meter.

Where the atmosphere blasts out of the end of the worm hole into space. But after thinking about this for some time. I realize that earths gravity may well transverse the wormhole too. So you may get some atmosphere shooting into space, but it could form a spherical ball around the wormhole (Assuming the wormhole is spherical in effect). Held there by earths gravity, at some point these two forces would probably equalize.

If the wormhole hit[was on] the ground, I doubt anything special would happen. I don't think much dirt and rock would get sucked out into the void just by the shear vacuum of space. Again, because earth has enaugh gravity to hold this stuff normally and just a 1 meter area of vacuum probably wont overcome that.

So if you allow the vacuum of space to transverse the wormhole, you almost have to allow gravity and anything else to transfer too.

Some of this depends on how you define

other falls into Earth's gravity well

If you mean in orbit, this may not do anything. It's not like you can drain the gravity of the planet away. It might create a navigational hazard. At worst you would get a area on the opposite side of the wormhole that has a bit less gravity, like a stone in a river slows the river just behind the stone. This may be less noticeable the further away from the wormhole you go or there may be "hole" in earths gravity well where it's leaking though the worm hole.

$\begingroup$"If the wormhole hit the ground" what do you mean by "hit" the ground? What would stop it from going through the ground?$\endgroup$
– PyRulezFeb 4 '18 at 5:40

$\begingroup$- Um "the ground" I thought this was pretty clear "Disregarding the mass/energy issue."$\endgroup$
– ArtisticPhoenixFeb 4 '18 at 5:41

$\begingroup$what force I mean. Gravity doesn't stop working when you touch the ground.$\endgroup$
– PyRulezFeb 4 '18 at 5:42

$\begingroup$Who said it does, in fact that's exactly my point. The question states "other falls into Earth's gravity well" Which could be in orbit, in the atmosphere or on the ground.$\endgroup$
– ArtisticPhoenixFeb 4 '18 at 5:43

1

$\begingroup$Thats easy, its QSD or Quantum Slinky Dyamics, see as the quarks try to compact they cant and as they stretch apart they cant, so they just sort of rebound in the other direction. There was something about strings, and how they break into a helix (like a little spring) but I cant remember the specifics.$\endgroup$
– ArtisticPhoenixFeb 4 '18 at 5:54